--- a/src/HOL/UNITY/Rename.thy Tue May 17 10:19:46 2005 +0200
+++ b/src/HOL/UNITY/Rename.thy Tue May 17 17:01:19 2005 +0200
@@ -110,10 +110,10 @@
lemma bij_extend: "bij h ==> bij (extend (%(x,u::'c). h x))"
apply (rule bijI)
apply (blast intro: Extend.inj_extend)
-apply (rule_tac f = "extend (% (x,u) . inv h x) " in surjI)
-apply (simplesubst inv_inv_eq [of h, symmetric], assumption)
-apply (subst extend_inv, simp add: bij_imp_bij_inv)
-apply (simp add: inv_inv_eq)
+apply (rule_tac f = "extend (% (x,u) . inv h x)" in surjI)
+apply (subst (1 2) inv_inv_eq [of h, symmetric], assumption+)
+apply (simp add: bij_imp_bij_inv extend_inv [of "inv h"])
+apply (simp add: inv_inv_eq)
apply (rule Extend.extend_inverse)
apply (simp add: bij_imp_bij_inv)
done
@@ -146,14 +146,14 @@
lemma inj_rename_imp_inj: "inj (rename h) ==> inj h"
apply (unfold inj_on_def, auto)
-apply (drule_tac x = "mk_program ({x}, {}, {}) " in spec)
-apply (drule_tac x = "mk_program ({y}, {}, {}) " in spec)
+apply (drule_tac x = "mk_program ({x}, {}, {})" in spec)
+apply (drule_tac x = "mk_program ({y}, {}, {})" in spec)
apply (auto simp add: program_equality_iff rename_def extend_def)
done
lemma surj_rename_imp_surj: "surj (rename h) ==> surj h"
apply (unfold surj_def, auto)
-apply (drule_tac x = "mk_program ({y}, {}, {}) " in spec)
+apply (drule_tac x = "mk_program ({y}, {}, {})" in spec)
apply (auto simp add: program_equality_iff rename_def extend_def)
done